Please explain how $12,905.80 is the answer to the question: To save for retirement, a couple deposits $4000 in their account that pays 5.9% interest compounded quarterly. What will be the value of thier investment in 20 years?

4000*[1 + 0.059/4)]^80 = 12,905.80

You need a calculator to take the 80th power of 1.01475, otherwise it would take all day by hand. You could also use Google. (Just type 1.01475^80 in the Search window)

The 80th power is needed because there are 80 interest payment periods in 20 years.